A new integral representation of the Riemann zeta function

摘要

The series SigmaZ(n=1)(infinity)(1(l+1))e(-zkk), k is any positive integer, l is a positive odd number and l less than or equal to 2k - 1, is studied, and for each pair (k, l), an integral representation of the Riemann zeta function is given. For small pairs, this provides known representations.